Year: 2023
Type: article
Abstract: The Markov property is widely imposed in analysis of time series data. Correspondingly, testing the Markov property, and relatedly, inferring the order of a Markov model, are of paramount importance. In this article, we propose a nonparametric test for the Markov property in high-dimensional time series via deep conditional generative learning. We also apply the test sequentially to determine the order of the Markov model. We show that the test controls the type-I error asymptotically, and has the power approaching one. Our proposal makes novel contributions in several ways. We utilise and extend state-of-the-art deep generative learning to estimate the conditional density functions, and establish a sharp upper bound on the approximation error of the estimators. We derive a doubly robust test statistic, which employs a nonparametric estimation but achieves a parametric convergence rate. We further adopt sample splitting and cross-fitting to minimise the conditions required to ensure the consistency of the test. We demonstrate the efficacy of the test through both simulations and the three data applications.
Authors: Yunzhe Zhou, Chengchun Shi, Lexin Li, Qiwei Yao
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,985
Awards: Statistical Methods in Offline Reinforcement Learning, G4402519365, Statistical Network Analysis: Model Selection, Differential Privacy, and Dynamic Structures, New Statistical Methods for Multicenter Multimodal Longitudinal Neuroimaging Analysis, Network Stochastic Processes and Time Series (NeST), G6692605481, Mechanisms of Alzheimer's Disease Progression in the Aging Brain, G7054964240, CIF: Small: Collaborative Research: Graphical Modeling of Multivariate Functional Data, G8659321454
OpenAlex ID: W4381848600